Tests confirmed the presence of Naegleria fowleri in the system. The amoeba can cause an infection of the brain, which is usually fatal.
Infections are rare in the US, with 34 reported between 2009 and 2018.
Officials in Lake Jackson said they were disinfecting the water supply but did not know how long this would take.
Eight Texas communities were originally told on Friday night not to use their water supply for any reason except to flush toilets. The warning was lifted on Saturday for everywhere but Lake Jackson, a city of more than 27,000 residents.
Authorities in Lake Jackson later said that people could begin using the water, but must boil it before drinking it. Residents were also told to take other measures, including not allowing water to go up their noses while showering or bathing.
The city warned that children, elderly people, and people with weakened immune systems were “particularly vulnerable”.
Officials said they were flushing the water system, and would then carry out tests to ensure the water was safe to use.
An investigation into the city’s water supply began after a six-year-old boy contracted the microbe and died earlier this month, Lake Jackson City Manager Modesto Mundo told reporters.
The Centers for Disease Control and Prevention (CDC) says infection typically occurs when people go swimming or diving in “warm freshwater places”.
The CDC says people cannot get infected by swallowing contaminated water, and it cannot be passed from person to person.
Those infected with Naegleria fowleri have symptoms including fever, nausea and vomiting, as well as a stiff neck and headaches. Most die within a week.